1. Field of the Invention
The present invention relates to target tracking systems; and more particularly to an improved Kalman estimator system for predicting the position of moving targets.
2. Description of the Prior Art
In a typical radar tracking system, pulses are transmitted through an antenna at a predetermined repetition rate towards a target. The target reflects the pulses back to the antenna. The time of reception and the doppler shift of the pulses, together with the pointing angles of the airborne antenna, the time history of angular orientation and of the velocity vector of the tracking aircraft are processed by a signal processor to generate signals that represent range, radial velocity or range rate, and the elevation and azimuth angles to the target.
In the mechanization of such a system, a high speed digital computer may be used that operates upon the measured input signals every two hundredths of a second, for example. The range measurement signals may be read by the computer every four hundredths of a second, and the angle measurements may be calculated every four hundredths of a second during alternate cycles of calculation. The results of each calculation may be output to the antenna once every five thousandths of a second for controlling the antenna position to track the target.
From the input information, estimates or predictions of target position are generated at predetermined fractions of a second; and such target position estimation signals are calculated from the last estimated position, target velocity, and target acceleration estimation signals, and are utilized to point the antenna at the moving target; and, also may be utilized to control the pointing of an implement at the target, if desired. An optimal estimating system that is well suited for program implementation in a high speed digital computer is the estimator known as a Kalman filter. The Kalman filter is well known in the literature and may be defined as an optimal recursive filter that is based on space and time domain formulations.
Briefly, such a Kalman filter or estimator processes the measured information concerning moving targets such as range, radial velocity, elevation, and azimuth to develop signals that represent estimates of target relative position, target relative velocity and target acceleration. An additional set of parameters is developed representing the uncertainty in the estimation of target position and its time derivatives (rates of change with respect to time). The elements of this set of parameters are called the error covariances of the estimation model. A second set of error covariances represents the mean squared error in measurement of range, radial velocity, azimuth and elevation. Any difference between a predicted value of an estimated quantity and its measured value is commonly called a residual. This residual is composed of errors in estimation and errors in measurement. Obviously, not all of an observed residual should be used to correct errors in estimation, since the residual contains measurement errors. A Kalman gain factor is formulated which seeks to take that fraction of a residual which is due to estimation error alone. This fraction of the residual is then used to revise the estimation model after each observation, or measurement. The revised estimates are then used to predict the result of the next measurement, and the process is repeated.
The measured quantities as well as the quantities for predicting the position of the target must be referenced to a coordinate system. For example, a geographic coordinate system extends along north, east, and down axes (NED) respectively, or a line-of-sight (LOS) or antenna coordinate system, which extends along three axes, the direction that the antenna is pointing (i), orthogonally to the right of te antenna (j), and downward from such direction (k). A further coordinate system is referred to as an aircraft coordinate system which extends along dead ahead, right, and down axes (XYZ) from the nose of the aircraft, respectively. These coordinate systems may be utilized in the tracking operation of the antenna and the pointing of an implement at a target. For example, signals may be generated that are representative of the attitude of the aircraft relative to the horizon; that is, nose up or nose down, as well as signals representative of the velocity of the aircraft. These signals, as well as tracking error signals of the antenna, are input to and operated upon by the digital computer to calculate the various output signals for positioning the antenna to maintain its track on the target.
The use of a stable (e.g., geographic) coordinate system as a reference frame allows the formulation of a linear dynamic model. This results in the simplest sequence of calculations while inherently providing more accurate predictions of target position, velocity and acceleration. Also, with availability of measured attitude with respect to the stable reference, rate gyros are not required to measure its time rate of change of orientation. Measured quantities such as range, range rate and elevation and azimuth angles are interdependent when calculating target position, velocity and acceleration. Thus, for n interdependent parameters there would be n.times.n sets of calculations involved in the direct generation of the Kalman gain factors. For the three spatial components (north, east and down) of target position, velocity and acceleration, n equal nine.
In the line-of-sight (LOS) coordinate system, the measured quantities range, range rate and azimuth and elevation angles are independent of each other. The Kalman gain computations are greatly simplified; and the number of such computations are greatly reduced. If the radar beam shape is the same in azimuth and elevation, the number of computations is further reduced. However, the orientation of the LOS system moves with time as the antenna-carrying aircraft moves in three-dimensional space. In conventional systems, formulated wholly within the LOS coordinate system, this change in the LOS orientation customarily employs rate gyros to measure the reorientation and results in a nonlinear system model to predict the target's position, velocity and acceleration. The nonlinear system models require more complex computations involving complicated weighting factors to predict target position, velocity and acceleration.
Thus, it is desirable to provide an improved system utilizing a Kalman estimator that has the advantages of both a stable and a line-of-sight coordinate system without the inherent disadvantages of either.